# Classical Covariant fields

This books discusses the classical foundations of field theory, using the language of variational methods and covariance. These notions have a deep and important connection with the second quantized field theory, shown to follow from the Schwinger Action Principle. This book takes a pragmatic view of field theory, focusing on issues which are normally omitted from quantum field theory texts.

#### Typographical / cut-paste / editorial errors

- On p. 18, eqn. 2.49 should have a mu index on the RHS, not k.
- On p. 59, eqn 4.43, the integral limits have gone walkabout...!
- On p.114, Para 4, "their full description...." should begin with a capital letter
- On p. 169, line 5 "which explain" should be "and explains".
- On p.178-179, eqn. (8.30), delta theta/N should be theta/N, and the entire large paentheses should be raised to the N-th power.
- On p.178, (8.27) and (8.28), replace T_A with iT_A, for consistency with following page and rest of book.
- Pn p. 472, second bullet, some text "common situtation" has accidentally been pasted in.

#### Textual ambiguities

The final production font is different to that which was used during proof reading. That makes some things look nicer and others look worse. In particular, it is not always possible to see when a Greek letter is in boldface, i.e. the vector form versus a scalar form. Since I have made a distinction between vector and scalar sigma measures for spatial surface and volume elements, this can lead to confusion.

- On p.16, it is stated that the pseudo-scalar
**E.B**vanishes for a self-consistent field. This is rather misleading and the sentence should probably be deleted. The point is that the term exists only on the surface of a region of space, and thus, in any finite volume with a boundary, requires a "breaking" of the Lorentz symmetry by the boundary to have a non-zero contribution. Since many applications of electromagnetism work by breaking the symmetry, this comment seems unhelpful. However, in the context of the kinds of studies this book addresses, it is not incorrect. - On p. 20, eqn 2.58 would be better with volume integrals written (d
**x**) instead of with Greek sigma. Although the latter is correct according to the notation guide on p. 405, this is the first time we meet this notation and it is not easy to distinguish the scale sigma from a bold vector sigma in the preceding equation (2.57). This has resulted in some confusion (cf the scathing remarks of Milton in his review, SIAM Reviews - see below).